Which statement best describes a non-singular matrix?

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Multiple Choice

Which statement best describes a non-singular matrix?

Explanation:
Non-singular means you can reverse what the matrix does. For a square matrix, that means there exists another matrix that undoes it, giving the identity—this is the inverse. Equivalently, a non-singular matrix has a nonzero determinant and its columns are linearly independent. So the statement that best describes it is that it has an inverse. If the determinant were zero, it would be singular and not invertible. Being non-square (more rows than columns) or being symmetric doesn’t determine invertibility on its own.

Non-singular means you can reverse what the matrix does. For a square matrix, that means there exists another matrix that undoes it, giving the identity—this is the inverse. Equivalently, a non-singular matrix has a nonzero determinant and its columns are linearly independent. So the statement that best describes it is that it has an inverse. If the determinant were zero, it would be singular and not invertible. Being non-square (more rows than columns) or being symmetric doesn’t determine invertibility on its own.

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